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The area of the triangle is equal to the area of the trapezium - OCR - GCSE Maths - Question 15 - 2020 - Paper 3

Question 15

The area of the triangle is equal to the area of the trapezium. Calculate the height, h cm, of the trapezium.

Worked Solution & Example Answer:The area of the triangle is equal to the area of the trapezium - OCR - GCSE Maths - Question 15 - 2020 - Paper 3

Step 1

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Answer

The formula for the area of a triangle is given by:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

In this case, the base is 9 cm and the height is 8 cm:

$\text{Area}_{triangle} = \frac{1}{2} \times 9 \times 8 = 36\text{ cm}^2$

Step 2

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Answer

The area of a trapezium is calculated using the formula:

$\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{height}$

For the given trapezium, the bases are 12 cm and 20 cm, and the height is h cm:

$\text{Area}_{trapezium} = \frac{1}{2} \times (12 + 20) \times h = \frac{1}{2} \times 32 \times h = 16h\text{ cm}^2$

Step 3

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Answer

Since the area of the triangle is equal to the area of the trapezium, we can set up the equation:

$36 = 16h$

Step 4

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Answer

To solve for h, divide both sides of the equation by 16:

$h = \frac{36}{16} = 2.25\text{ cm}$

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